Non-isothennal plasma modification of polymer surfaces is of scientific and technological interest, since it can be used to improve wettability, adliesion, etc. This thesis covers three main areas, firstly a study of the processes occuixing at the plasma - polymer interface using a newly developed technique, secondly the fluorination of polymer surfaces using a novel transportable reagent and lastly the oxidation of rubber substrates. The interaction of N(_2), O(_2), air and H(_2) glow discharges with polyethylene surfaces has been studied using a newly developed mass spectrometric technique. The species permeating through to the reverse side of the polymer substrate can be detected and characterised. Compared to previously reported approaches, this method is capable of sampling reaction products within closer proximity to the plasma - polymer interface, thereby circumventing the complication of primary product species undergoing secondary processes within the bulk of the electrical discharge prior to detection. The nature of the feed gas is found to strongly influence the chemical reaction pathways occurring at the plasma - polymer interface. Xenon difluoride (XeF(_2)) plasma treatment of a series of polymers containing different repeat units gives rise to surface fluorination. A comparison with CF(_4) plasma modification shows that XeF(_2) electrical discharges are more effective at fluorinating polymers. The extent of fluorine incorporation can be accounted for in terms of a structure-behaviour relationship derived from extended Huckel molecular orbital calculations. Exposure of polyethylene and polystyrene to xenon difluoride (XeF(_2)) in the presence of vacuum ultraviolet (VUV) irradiation also causes surface fluorination. The extent of reaction is found to depend upon the VUV absorption characteristics of the XeF(_2) feed gas as well as those of the polymer substrate. Low pressure glow discharge, dielectric barrier discharge and ozone treatments all oxidise additive-free rubber substrates. The oxidation susceptibility of the rubber substrates differed during all three treatments, and was found to be dependent upon the concentration of unsaturated carbons, saturated carbons and phenyl rings. The additives placed ill rubbers to improve properties such as tear resistance influence their degree of oxidation.